Hardy-Sobolev Type Inequalities with Sharp Constants in Carnot-Carath,odory Spaces

被引：26
|
作者：
Danielli, Donatella [1 ]
Garofalo, Nicola [1 ]
Phuc, Nguyen Cong [2 ]
机构：
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
来源：
POTENTIAL ANALYSIS | 2011年 / 34卷 / 03期
基金：
美国国家科学基金会;
关键词：
Hardy type inequalities; Carnot groups; Carnot-Carathcodory spaces; Horizontal p-Laplacian; CARNOT-CARATHEODORY SPACES; HEISENBERG-GROUP; VECTOR-FIELDS; SUBELLIPTIC EQUATIONS; FUNDAMENTAL-SOLUTIONS; UNIQUE CONTINUATION; HEAT-EQUATION; OPERATORS; THEOREMS; SURFACE;
D O I：
10.1007/s11118-010-9190-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a generalization with sharp constants of a classical inequality due to Hardy to Carnot groups of arbitrary step, or more general Carnot-Carath,odory spaces associated with a system of vector fields of Hormander type. Under a suitable additional assumption (see Eq. 1.6 below) we are able to extend such result to the nonlinear case p not equal 2. We also obtain a sharp inequality of Hardy-Sobolev type.
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页码：223 / 242
页数：20
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